It may have been the biggest all-female demonstration in Egypt's history.

Clinton on Tuesday condemned as "particularly shocking" incidents such as one in which two Egyptian soldiers were filmed dragging a woman protester on the ground by her black full-body veil, exposing her bra, then clubbing and kicking her.

The confrontations provide a turbulent backdrop to Egypt's progress towards democracy, with nine provinces, mostly outside the capital, holding run-off votes on Wednesday and Thursday in a parliamentary election being staggered over six weeks.

The army has pledged to hand power to an elected president by July, but its plans to permanently shield itself from civilian oversight in the new constitution have enraged pro-democracy protesters, who want it to hand over power at once.

Medical sources say 13 people have been killed and hundreds wounded in the latest violence, which began on Friday in Tahrir and nearby streets leading to parliament and the cabinet office.

"Women protesters have been rounded up and subjected to horrific abuse. Journalists have been sexually assaulted. And now women are being attacked, stripped and beaten in the streets," Clinton said in a speech at Washington's Georgetown University on Monday.

"This systematic degradation of Egyptian women dishonours the revolution, disgraces the state and its uniform and is not worthy of a great people," she added, in some of the strongest U.S. criticism of Egypt's new rulers.

Gunfire rang out across the square at dawn as security forces charged hundreds of protesters, and later thousands of women marched on the square to condemn attacks on females who have taken part in the protests. But by nightfall the square was calm again.

The women marchers were dressed in black and accompanied by male demonstrators who vowed to protect them from harassment.

"The women of Egypt are a red line!" they chanted.

"This is a continuation of the systematic violence we used to witness (under Mubarak)," said Sarah Rifaat, a 27-year-old environmentalist. "They manipulate women, thinking they can break the people and scare them this way.

"What happened to the girl who was stripped and dragged was sheer savagery. We cannot be silent about this. I want someone from the military council to admit responsibility."

In a statement, the army council that took over after Mubarak was overthrown in February apologised, saying it "respects and appreciates Egyptian women and their right to protest and fully participate in political life".

General Adel Emara, a member of the council, said on Monday that the attack on the woman protester was an isolated incident and was under investigation. He denied that the army had given orders to clear the square.

But other generals and their advisers have condemned the pro-democracy protesters, sometimes in extraordinary terms.

"What is your feeling when you see Egypt and its history burn in front of you?" retired general Abdel Moneim Kato, an army adviser, told the daily al-Shorouk, referring to a historic archive building set alight during clashes - the Institute of Egypt. "Yet you worry about a vagrant who should be burnt in Hitler's incinerators."

One opposition group that has lowered its profile in the protests is the once-banned Muslim Brotherhood, whose Freedom and Justice Party leads the election results after the first round, followed by hardline Salafi Islamists.

A large percentage of the individual - rather than party list - seats up for grabs in the run-offs will be contested between Muslim Brotherhood and Salafi candidates.

Washington has reached out to Islamists in a shift in approach since the summer. A senior U.S. diplomat met Islamist and other newly elected members of parliament in the northern city of Alexandria, the embassy said on Tuesday. (Writing by Kevin Liffey; Editing by Michael Roddy)